Dense Matrix and Vector Template Library

Type traits to retrieve the field and the real type of classes. More...

Files
file	densematrix.hh
	Implements a matrix constructed from a given type representing a field and a compile-time given number of rows and columns.
file	densevector.hh
	Implements the dense vector interface, with an exchangeable storage class.
file	dynmatrix.hh
	This file implements a dense matrix with dynamic numbers of rows and columns.
file	dynvector.hh
	This file implements a dense vector with a dynamic size.
file	fmatrix.hh
	Implements a matrix constructed from a given type representing a field and compile-time given number of rows and columns.
file	fvector.hh
	Implements a vector constructed from a given type representing a field and a compile-time given size.
file	scalarmatrixview.hh
	Implements a scalar matrix view wrapper around an existing scalar.
file	scalarvectorview.hh
	Implements a scalar vector view wrapper around an existing scalar.

Namespaces
namespace	Dune
	Dune namespace.
namespace	Dune::MathOverloads
	namespace for customization of math functions with Dune-Semantics

Classes
struct	Dune::DenseMatrixAssigner< DenseMatrix, RHS >
	you have to specialize this structure for any type that should be assignable to a DenseMatrix More...
class	Dune::FMatrixError
	Error thrown if operations of a FieldMatrix fail. More...
class	Dune::DenseMatrix< MAT >
	A dense n x m matrix. More...
class	Dune::DenseIterator< C, T, R >
	Generic iterator class for dense vector and matrix implementations. More...
class	Dune::DenseVector< V >
	Interface for a class of dense vectors over a given field. More...
class	Dune::DiagonalMatrix< K, n >
	A diagonal matrix of static size. More...
class	Dune::ContainerWrapperIterator< CW, T, R >
	Iterator class for sparse vector-like containers. More...
class	Dune::DynamicMatrix< K >
	Construct a matrix with a dynamic size. More...
class	Dune::DynamicVector< K, Allocator >
	Construct a vector with a dynamic size. More...
class	Dune::FieldMatrix< K, ROWS, COLS >
	A dense n x m matrix. More...
class	Dune::FieldVector< K, SIZE >
	vector space out of a tensor product of fields. More...
struct	Dune::IsFieldVectorSizeCorrect< C, SIZE >
	TMP to check the size of a DenseVectors statically, if possible. More...
class	Dune::FMatrixPrecision< ctype >
	Precisions for calculations with FieldMatrix and FieldVector. More...

Typedefs
typedef K	Dune::DiagonalMatrix< K, n >::value_type
	export the type representing the field
typedef K	Dune::DiagonalMatrix< K, n >::block_type
	export the type representing the components
typedef std::size_t	Dune::DiagonalMatrix< K, n >::size_type
	The type used for the index access and size operations.
typedef DiagonalRowVector< K, n >	Dune::DiagonalMatrix< K, n >::row_type
	Each row is implemented by a field vector.
typedef ContainerWrapperIterator< const WrapperType, reference, reference >	Dune::DiagonalMatrix< K, n >::Iterator
	Iterator class for sequential access.
typedef Iterator	Dune::DiagonalMatrix< K, n >::iterator
	typedef for stl compliant access
typedef Iterator	Dune::DiagonalMatrix< K, n >::RowIterator
	rename the iterators for easier access
typedef row_type::Iterator	Dune::DiagonalMatrix< K, n >::ColIterator
	rename the iterators for easier access
typedef ContainerWrapperIterator< const WrapperType, const_reference, const_reference >	Dune::DiagonalMatrix< K, n >::ConstIterator
	Iterator class for sequential access.
typedef ConstIterator	Dune::DiagonalMatrix< K, n >::const_iterator
	typedef for stl compliant access
typedef ConstIterator	Dune::DiagonalMatrix< K, n >::ConstRowIterator
	rename the iterators for easier access
typedef const_row_type::ConstIterator	Dune::DiagonalMatrix< K, n >::ConstColIterator
	rename the iterators for easier access
typedef K	Dune::DiagonalRowVectorConst< K, n >::field_type
	export the type representing the field
typedef K	Dune::DiagonalRowVectorConst< K, n >::block_type
	export the type representing the components
typedef std::size_t	Dune::DiagonalRowVectorConst< K, n >::size_type
	The type used for the index access and size operation.
typedef ContainerWrapperIterator< DiagonalRowVectorConst< K, n >, const K, const K & >	Dune::DiagonalRowVectorConst< K, n >::ConstIterator
	ConstIterator class for sequential access.
typedef ConstIterator	Dune::DiagonalRowVectorConst< K, n >::const_iterator
	typedef for stl compliant access
typedef K	Dune::DiagonalRowVector< K, n >::field_type
	export the type representing the field
typedef K	Dune::DiagonalRowVector< K, n >::block_type
	export the type representing the components
typedef std::size_t	Dune::DiagonalRowVector< K, n >::size_type
	The type used for the index access and size operation.
typedef ContainerWrapperIterator< DiagonalRowVector< K, n >, K, K & >	Dune::DiagonalRowVector< K, n >::Iterator
	Iterator class for sequential access.
typedef Iterator	Dune::DiagonalRowVector< K, n >::iterator
	typedef for stl compliant access
typedef ContainerWrapperIterator< DiagonalRowVectorConst< K, n >, const K, const K & >	Dune::DiagonalRowVector< K, n >::ConstIterator
	ConstIterator class for sequential access.
typedef ConstIterator	Dune::DiagonalRowVector< K, n >::const_iterator
	typedef for stl compliant access

Enumerations
enum	{ Dune::DiagonalMatrix< K, n >::blocklevel = 1 }
	We are at the leaf of the block recursion. More...
enum	{ Dune::DiagonalMatrix< K, n >::rows = n , Dune::DiagonalMatrix< K, n >::cols = n }
	export size More...
enum	{ Dune::DiagonalRowVectorConst< K, n >::blocklevel = 1 }
	We are at the leaf of the block recursion. More...
enum	{ Dune::DiagonalRowVectorConst< K, n >::size = n }
	export size More...

Functions
template<typename MAT >
std::ostream &	Dune::operator<< (std::ostream &s, const DenseMatrix< MAT > &a)
	Sends the matrix to an output stream.
constexpr	Dune::DiagonalMatrix< K, n >::DiagonalMatrix ()=default
	Default constructor.
	Dune::DiagonalMatrix< K, n >::DiagonalMatrix (const K &k)
	Constructor initializing the whole matrix with a scalar.
	Dune::DiagonalMatrix< K, n >::DiagonalMatrix (const FieldVector< K, n > &diag)
	Constructor initializing the diagonal with a vector.
	Dune::DiagonalMatrix< K, n >::DiagonalMatrix (std::initializer_list< K > const &l)
	Construct diagonal matrix from an initializer list. More...
DiagonalMatrix &	Dune::DiagonalMatrix< K, n >::operator= (const K &k)
	Assignment from a scalar.
bool	Dune::DiagonalMatrix< K, n >::identical (const DiagonalMatrix< K, n > &other) const
	Check if matrix is the same object as the other matrix.
Iterator	Dune::DiagonalMatrix< K, n >::begin ()
	begin iterator
Iterator	Dune::DiagonalMatrix< K, n >::end ()
	end iterator
Iterator	Dune::DiagonalMatrix< K, n >::beforeEnd ()
Iterator	Dune::DiagonalMatrix< K, n >::beforeBegin ()
ConstIterator	Dune::DiagonalMatrix< K, n >::begin () const
	begin iterator
ConstIterator	Dune::DiagonalMatrix< K, n >::end () const
	end iterator
ConstIterator	Dune::DiagonalMatrix< K, n >::beforeEnd () const
ConstIterator	Dune::DiagonalMatrix< K, n >::beforeBegin () const
DiagonalMatrix &	Dune::DiagonalMatrix< K, n >::operator+= (const DiagonalMatrix &y)
	vector space addition
DiagonalMatrix &	Dune::DiagonalMatrix< K, n >::operator-= (const DiagonalMatrix &y)
	vector space subtraction
DiagonalMatrix &	Dune::DiagonalMatrix< K, n >::operator+= (const K &k)
	vector space multiplication with scalar
DiagonalMatrix &	Dune::DiagonalMatrix< K, n >::operator-= (const K &k)
	vector space division by scalar
DiagonalMatrix &	Dune::DiagonalMatrix< K, n >::operator*= (const K &k)
	vector space multiplication with scalar
DiagonalMatrix &	Dune::DiagonalMatrix< K, n >::operator/= (const K &k)
	vector space division by scalar
bool	Dune::DiagonalMatrix< K, n >::operator== (const DiagonalMatrix &other) const
	comparison operator
bool	Dune::DiagonalMatrix< K, n >::operator!= (const DiagonalMatrix &other) const
	incomparison operator
template<class X , class Y >
void	Dune::DiagonalMatrix< K, n >::mv (const X &x, Y &y) const
	y = A x
template<class X , class Y >
void	Dune::DiagonalMatrix< K, n >::mtv (const X &x, Y &y) const
	y = A^T x
template<class X , class Y >
void	Dune::DiagonalMatrix< K, n >::umv (const X &x, Y &y) const
	y += A x
template<class X , class Y >
void	Dune::DiagonalMatrix< K, n >::umtv (const X &x, Y &y) const
	y += A^T x
template<class X , class Y >
void	Dune::DiagonalMatrix< K, n >::umhv (const X &x, Y &y) const
	y += A^H x
template<class X , class Y >
void	Dune::DiagonalMatrix< K, n >::mmv (const X &x, Y &y) const
	y -= A x
template<class X , class Y >
void	Dune::DiagonalMatrix< K, n >::mmtv (const X &x, Y &y) const
	y -= A^T x
template<class X , class Y >
void	Dune::DiagonalMatrix< K, n >::mmhv (const X &x, Y &y) const
	y -= A^H x
template<class X , class Y >
void	Dune::DiagonalMatrix< K, n >::usmv (const typename FieldTraits< Y >::field_type &alpha, const X &x, Y &y) const
	y += alpha A x
template<class X , class Y >
void	Dune::DiagonalMatrix< K, n >::usmtv (const typename FieldTraits< Y >::field_type &alpha, const X &x, Y &y) const
	y += alpha A^T x
template<class X , class Y >
void	Dune::DiagonalMatrix< K, n >::usmhv (const typename FieldTraits< Y >::field_type &alpha, const X &x, Y &y) const
	y += alpha A^H x
double	Dune::DiagonalMatrix< K, n >::frobenius_norm () const
	frobenius norm: sqrt(sum over squared values of entries)
double	Dune::DiagonalMatrix< K, n >::frobenius_norm2 () const
	square of frobenius norm, need for block recursion
double	Dune::DiagonalMatrix< K, n >::infinity_norm () const
	infinity norm (row sum norm, how to generalize for blocks?)
double	Dune::DiagonalMatrix< K, n >::infinity_norm_real () const
	simplified infinity norm (uses Manhattan norm for complex values)
template<class V >
void	Dune::DiagonalMatrix< K, n >::solve (V &x, const V &b) const
	Solve system A x = b.
void	Dune::DiagonalMatrix< K, n >::invert ()
	Compute inverse.
K	Dune::DiagonalMatrix< K, n >::determinant () const
	calculates the determinant of this matrix
static constexpr size_type	Dune::DiagonalMatrix< K, n >::N ()
	number of blocks in row direction
static constexpr size_type	Dune::DiagonalMatrix< K, n >::M ()
	number of blocks in column direction
bool	Dune::DiagonalMatrix< K, n >::exists (size_type i, size_type j) const
	return true when (i,j) is in pattern
reference	Dune::DiagonalMatrix< K, n >::operator[] (size_type i)
	Return reference object as row replacement.
const_reference	Dune::DiagonalMatrix< K, n >::operator[] (size_type i) const
	Return const_reference object as row replacement.
const K &	Dune::DiagonalMatrix< K, n >::diagonal (size_type i) const
	Get const reference to diagonal entry.
K &	Dune::DiagonalMatrix< K, n >::diagonal (size_type i)
	Get reference to diagonal entry.
const FieldVector< K, n > &	Dune::DiagonalMatrix< K, n >::diagonal () const
	Get const reference to diagonal vector.
FieldVector< K, n > &	Dune::DiagonalMatrix< K, n >::diagonal ()
	Get reference to diagonal vector.
	Dune::DiagonalRowVectorConst< K, n >::DiagonalRowVectorConst ()
	Constructor making uninitialized vector.
	Dune::DiagonalRowVectorConst< K, n >::DiagonalRowVectorConst (K *p, int col)
	Constructor making vector with identical coordinates.
const K &	Dune::DiagonalRowVectorConst< K, n >::operator[] (size_type i) const
	same for read only access
ConstIterator	Dune::DiagonalRowVectorConst< K, n >::begin () const
	begin ConstIterator
ConstIterator	Dune::DiagonalRowVectorConst< K, n >::end () const
	end ConstIterator
ConstIterator	Dune::DiagonalRowVectorConst< K, n >::beforeEnd () const
ConstIterator	Dune::DiagonalRowVectorConst< K, n >::beforeBegin () const
bool	Dune::DiagonalRowVectorConst< K, n >::operator== (const DiagonalRowVectorConst &y) const
	Binary vector comparison.
size_type	Dune::DiagonalRowVectorConst< K, n >::N () const
	number of blocks in the vector (are of size 1 here)
size_type	Dune::DiagonalRowVectorConst< K, n >::dim () const
	dimension of the vector space
size_type	Dune::DiagonalRowVectorConst< K, n >::rowIndex () const
	index of this row in surrounding matrix
const K &	Dune::DiagonalRowVectorConst< K, n >::diagonal () const
	the diagonal value
	Dune::DiagonalRowVector< K, n >::DiagonalRowVector ()
	Constructor making uninitialized vector.
	Dune::DiagonalRowVector< K, n >::DiagonalRowVector (K *p, int col)
	Constructor making vector with identical coordinates.
DiagonalRowVector &	Dune::DiagonalRowVector< K, n >::operator= (const K &k)
	Assignment operator for scalar.
K &	Dune::DiagonalRowVector< K, n >::operator[] (size_type i)
	random access
Iterator	Dune::DiagonalRowVector< K, n >::begin ()
	begin iterator
Iterator	Dune::DiagonalRowVector< K, n >::end ()
	end iterator
Iterator	Dune::DiagonalRowVector< K, n >::beforeEnd ()
Iterator	Dune::DiagonalRowVector< K, n >::beforeBegin ()
template<typename V >
std::ostream &	operator<< (std::ostream &s, const DenseVector< V > &v)
	Write a DenseVector to an output stream. More...
template<class K , class Allocator >
std::istream &	operator>> (std::istream &in, DynamicVector< K, Allocator > &v)
	Read a DynamicVector from an input stream. More...
template<class K , int SIZE>
std::istream &	operator>> (std::istream &in, FieldVector< K, SIZE > &v)
	Read a FieldVector from an input stream. More...

Detailed Description

Type traits to retrieve the field and the real type of classes.

Type Traits to retrieve types associated with an implementation of Dune::DenseVector or Dune::DenseMatrix.

Type traits to retrieve the field and the real type of classes e.g. that of FieldVector or FieldMatrix

you have to specialize this class for every implementation of DenseVector or DenseMatrix.

 
typedef ... derived_type;
typedef ... value_type;
typedef ... size_type;

Enumeration Type Documentation

anonymous enum

template<class K , int n>

anonymous enum

We are at the leaf of the block recursion.

Enumerator
blocklevel	The number of block levels we contain.

anonymous enum

template<class K , int n>

anonymous enum

export size

Enumerator
size	The size of this vector.

anonymous enum

template<class K , int n>

anonymous enum

We are at the leaf of the block recursion.

Enumerator
blocklevel	The number of block levels we contain. This is 1.

anonymous enum

template<class K , int n>

anonymous enum

export size

Enumerator
rows	The number of rows.
cols	The number of columns.

Function Documentation

beforeBegin() [1/4]

template<class K , int n>

Iterator Dune::DiagonalMatrix< K, n >::beforeBegin ( )

inline

Returns

an iterator that is positioned before the first row of the matrix.

beforeBegin() [2/4]

template<class K , int n>

Iterator Dune::DiagonalRowVector< K, n >::beforeBegin ( )

inline

Returns

an iterator that is positioned before the first row of the matrix.

beforeBegin() [3/4]

template<class K , int n>

ConstIterator Dune::DiagonalMatrix< K, n >::beforeBegin ( ) const

inline

Returns

an iterator that is positioned before the first row of the matrix.

beforeBegin() [4/4]

template<class K , int n>

ConstIterator Dune::DiagonalRowVectorConst< K, n >::beforeBegin ( ) const

inline

Returns

an iterator that is positioned before the first row of the matrix.

beforeEnd() [1/4]

template<class K , int n>

Iterator Dune::DiagonalMatrix< K, n >::beforeEnd ( )

inline

Returns

an iterator that is positioned before the end iterator of the rows, i.e. at the last row.

beforeEnd() [2/4]

template<class K , int n>

Iterator Dune::DiagonalRowVector< K, n >::beforeEnd ( )

inline

Returns

an iterator that is positioned before the end iterator of the rows, i.e. at the last row.

beforeEnd() [3/4]

template<class K , int n>

ConstIterator Dune::DiagonalMatrix< K, n >::beforeEnd ( ) const

inline

Returns

an iterator that is positioned before the end iterator of the rows. i.e. at the last row.

beforeEnd() [4/4]

template<class K , int n>

ConstIterator Dune::DiagonalRowVectorConst< K, n >::beforeEnd ( ) const

inline

Returns

an iterator that is positioned before the end iterator of the rows. i.e. at the row.

DiagonalMatrix()

template<class K , int n>

Dune::DiagonalMatrix< K, n >::DiagonalMatrix ( std::initializer_list< K > const &  l )

inline

Construct diagonal matrix from an initializer list.

The elements of the list are copied into the diagonal elements of the matrix. If the initializer list is shorter than the matrix diagonal (which has n elements), the remaining matrix diagonal elements are left uninitialized. If the initializer list is longer, than only the first n elements will be copied into the matrix diagonal.

References Dune::DenseVector< V >::begin(), Dune::Simd::Overloads::min(), and Dune::DiagonalMatrix< K, n >::rows.

operator<<()

template<typename V >

std::ostream & operator<< ( std::ostream &  s, const DenseVector< V > &  v  )

related

Write a DenseVector to an output stream.

Parameters

[in]	s	std :: ostream to write to
[in]	v	DenseVector to write

Returns

the output stream (s)

References Dune::DenseVector< V >::size().

operator>>() [1/2]

template<class K , class Allocator >

std::istream & operator>> ( std::istream &  in, DynamicVector< K, Allocator > &  v  )

related

Read a DynamicVector from an input stream.

Note

This operator is STL compilant, i.e., the content of v is only changed if the read operation is successful.

Parameters

[in]	in	std :: istream to read from
[out]	v	DynamicVector to be read

Returns

the input stream (in)

operator>>() [2/2]

template<class K , int SIZE>

std::istream & operator>> ( std::istream &  in, FieldVector< K, SIZE > &  v  )

related

Read a FieldVector from an input stream.

Note

This operator is STL compliant, i.e., the content of v is only changed if the read operation is successful.

Parameters

[in]	in	std :: istream to read from
[out]	v	FieldVector to be read

Returns

the input stream (in)